We prove that for any knot K, there exists a decomposition of the 3-sphere into tetrahedra such that a representative of K is formed from one vertex and one edge of the decomposition. The proof is constructive, and based on fully augmented links. We use our method to produce a family of simplicial triangulations of the 3-sphere with a loop of four edges representing a t-fold connected sum of the trefoil, whose number of tetrahedra grows linearly in t. This is best possible up to a constant factor.
Objective Motivational interviewing is an important skill taught to student pharmacists, however providing adequate practice and quality feedback in the didactic curriculum is challenging. Generative artificial intelligence (AI)-supported simulations may address some of these issues. The purpose of this study was to evaluate the impact of an educator-led, AI-supported simulation (ATLAS) on pharmacy students' confidence in motivational interviewing (MI) skills, and to determine the optimal timing for its integration, either before or after peer-based MI practice, to maximize impact of MI learning interventions. Methods Students were divided into two groups: Pathway A used ATLAS after doing practice interviews with peers; Pathway B used ATLAS before doing practice interviews with peers. Surveys measured MI confidence and attitudes at baseline and at key timepoints before and after ATLAS use and peer interviews, enabling comparison of confidence trajectories across both pathways. Results Students in Pathway B, who completed ATLAS followed by a peer interview, demonstrated gains in MI confidence (P = 0.0063). In contrast, Pathway A who completed a peer interview followed by ATLAS, did not show robust improvements in confidence (P = 0.68). These findings suggest that using ATLAS prior to peer interaction may better support confidence in MI skill acquisition. Qualitative feedback revealed that among students who commented on practice preferences, most favored ATLAS over peer interviews, citing its low-stakes environment and flexibility. Conclusion Educator-led, AI-supported simulation using ATLAS offers scalable, time-efficient and a pedagogically sound approach to enhancing MI training. Students who engaged with ATLAS prior to peer interviews reported the highest confidence gains, suggesting that early exposure to AI-supported practice may enhance learners' confidence and preparedness for MI conversations. These findings support the integration of structured, low-stakes simulation tools as valuable precursors to peer-based learning, enhancing confidence development during MI training in pharmacy students.
Objectives Out-of-pocket (OOP) costs and financial toxicity remain significant barriers to equitable cancer care globally. This review systematically identifies and compares survey-based approaches used to measure patient- and household-level OOP expenditures and financial burden across diverse cancer settings. Methods A systematic search (2021-2025) of PubMed, Embase, and EBSCO databases identified studies that used survey methodologies, including patient-reported outcome measure instruments to estimate OOP spending and financial toxicity among cancer patients. Two reviewers independently screened studies and extracted data on key methodological characteristics including instrument type, cost domains, recall periods, validation practices, and reporting conventions to compare measurement approaches across studies. Results Based on the eligibility criteria, 45 studies were included. Survey tools showed substantial heterogeneity in structure, terminology, and measurement practices. Studies differed widely in the cost domains captured (direct medical, direct nonmedical, and indirect costs) and used recall periods ranging from a few days to 156 months. Reporting of currency, cost year, and conversion methods was inconsistent. Most relied on bespoke, nonvalidated questionnaires to measure objective financial burden, whereas validated patient-reported outcome measures, such as the Comprehensive Score for Financial Toxicity (COST) measures, were used inconsistently for subjective financial distress. This methodological variation substantially limited comparability across studies and hindered synthesis of patient-level financial burden. Conclusions Survey-based methods for measuring OOP costs and financial burden in cancer care remain highly variable. Establishing minimum methodological and reporting standards for core cost domains, recall periods, and financial burden indicators may improve comparability of evidence while allowing context-specific adaptation across health systems.
Introduction A substantial proportion of e-bike injuries and fatalities occur in motor-vehicle lanes, where riders are exposed to mixed traffic and higher crash risk, potentially offsetting the health benefits of e-bike use. Notably, many riders still enter motor-vehicle lanes even when dedicated bicycle lanes are available. Such lane intrusion increases exposure to hazardous interactions with vehicles and diminishes the safety benefits of cycling infrastructure. Therefore, identifying psychological factors associated with lane intrusion is important for informing injury-prevention interventions. Methodology An online survey of 729 e-bike riders (650 valid for analysis) assessed self-reported e-bike lane intrusion behaviour (e-bike LIB) using a newly developed Riding Lane Intrusion Behaviour Questionnaire, and assessed infrastructure perception, perceived safety, perceived risk, and Theory of Planned Behaviour constructs. We combined multi-group structural equation modelling with explainable machine learning to examine theory-informed associations among infrastructure perception, key psychological constructs, and e-bike LIB, and to explore potential non-linear patterns. Results Attitude, perceived behavioural control, and subjective norms were positively associated with self-reported lane intrusion, with attitude showing the strongest association. Infrastructure perception was negatively associated with self-reported lane intrusion and exhibited a possible non-linear pattern, with larger marginal reductions at higher levels of infrastructure perception. As infrastructure perception increased from low levels, perceived safety increased while perceived risk decreased, and these perceptions were further associated with e-bike LIB primarily indirectly through attitude and perceived behavioural control. Conclusions E-bike LIB should be understood as a preventable mixed-traffic exposure rather than a neutral lane-choice decision. The findings suggest that infrastructure provision should be complemented by behavioural measures targeting favourable attitudes, overconfidence, and permissive social norms. In poorer riding environments, stricter enforcement and improvements to the perceived usability and visibility of existing facilities may help discourage non-compliance with available bicycle lanes.
The case of Félicien Kabuga before the International Residual Mechanism for Criminal Tribunals has cast light on the international criminal law framework governing situations in which an accused is found unfit to stand trial. The Trial Chamber's decision to institute an ‘alternative finding procedure’ in lieu of a criminal trial—later quashed by the Appeals Chamber as incompatible with the Mechanism's Statute—raised fundamental questions about how international courts should respond when an accused cannot meaningfully participate in their own trial, including whether a tribunal should relinquish or retain control over the case. The case also offered a timely opportunity, which the court ultimately did not take, to revisit applicable principles in light of evolving standards under the Convention on the Rights of Persons with Disabilities.
